Question

What is the wavelength of a beam of X-rays (in $\mathring{A}$ ) which is diffracted by a crystal in a direction making an angle of $60^{\circ}$ with the incident beam and corresponding to first order reflection from crystal lattice planes separated by $3 \times 10^{-10}\, m$ ?

Answer 1

The Bragg's angle is half the angle through which the beam is deviated. Thus, in this case, the Bragg's angle is
$\theta=1 / 2 \times 60^{\circ}=30^{\circ}$
Bragg's equation is given as: $2 d \sin \theta=n \lambda$
Here, $d=3 \times 10^{-10} m , \theta=30^{\circ} ; n=1, \lambda=$ ?
$\lambda =\frac{2 d \sin \theta}{n}=\frac{2 \times\left(3 \times 10^{-10}\right) \sin 30^{\circ}}{1} m $
$=3 \times 10^{-10} m =3 \,\mathring{A}$